author | paulson |
Mon, 07 Oct 1996 10:28:44 +0200 | |
changeset 2056 | 93c093620c28 |
parent 1461 | 6bcb44e4d6e5 |
child 2275 | dbce3dce821a |
permissions | -rw-r--r-- |
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(* Title: HOLCF/one.thy |
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ID: $Id$ |
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Author: Franz Regensburger |
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Copyright 1993 Technische Universitaet Muenchen |
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Lemmas for one.thy |
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*) |
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open One; |
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(* ------------------------------------------------------------------------ *) |
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(* Exhaustion and Elimination for type one *) |
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(* ------------------------------------------------------------------------ *) |
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qed_goalw "Exh_one" One.thy [one_def] "z=UU | z = one" |
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(fn prems => |
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[ |
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(res_inst_tac [("p","rep_one`z")] liftE1 1), |
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(rtac disjI1 1), |
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(rtac ((abs_one_iso RS allI) RS ((rep_one_iso RS allI) RS iso_strict ) |
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RS conjunct2 RS subst) 1), |
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(rtac (abs_one_iso RS subst) 1), |
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(etac cfun_arg_cong 1), |
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(rtac disjI2 1), |
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(rtac (abs_one_iso RS subst) 1), |
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(rtac cfun_arg_cong 1), |
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(rtac (unique_void2 RS subst) 1), |
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(atac 1) |
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]); |
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qed_goal "oneE" One.thy |
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"[| p=UU ==> Q; p = one ==>Q|] ==>Q" |
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(fn prems => |
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[ |
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(rtac (Exh_one RS disjE) 1), |
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(eresolve_tac prems 1), |
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(eresolve_tac prems 1) |
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]); |
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(* ------------------------------------------------------------------------ *) |
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(* distinctness for type one : stored in a list *) |
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(* ------------------------------------------------------------------------ *) |
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val dist_less_one = [ |
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prove_goalw One.thy [one_def] "~one << UU" |
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(fn prems => |
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[ |
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(rtac classical3 1), |
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(rtac less_lift4b 1), |
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(rtac (rep_one_iso RS subst) 1), |
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(rtac (rep_one_iso RS subst) 1), |
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(rtac monofun_cfun_arg 1), |
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(etac ((abs_one_iso RS allI) RS ((rep_one_iso RS allI) RS iso_strict ) |
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RS conjunct2 RS ssubst) 1) |
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]) |
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]; |
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val dist_eq_one = [prove_goal One.thy "one~=UU" |
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(fn prems => |
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[ |
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(rtac not_less2not_eq 1), |
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(resolve_tac dist_less_one 1) |
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])]; |
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val dist_eq_one = dist_eq_one @ (map (fn thm => (thm RS not_sym)) dist_eq_one); |
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(* ------------------------------------------------------------------------ *) |
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(* one is flat *) |
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(* ------------------------------------------------------------------------ *) |
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qed_goalw "flat_one" One.thy [is_flat_def] "is_flat(one)" |
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(fn prems => |
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(rtac allI 1), |
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(rtac allI 1), |
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(res_inst_tac [("p","x")] oneE 1), |
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(Asm_simp_tac 1), |
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(res_inst_tac [("p","y")] oneE 1), |
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(asm_simp_tac (!simpset addsimps dist_less_one) 1), |
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(Asm_simp_tac 1) |
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]); |
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(* ------------------------------------------------------------------------ *) |
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(* properties of one_when *) |
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(* here I tried a generic prove procedure *) |
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(* ------------------------------------------------------------------------ *) |
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fun prover s = prove_goalw One.thy [one_when_def,one_def] s |
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(fn prems => |
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(simp_tac (!simpset addsimps [(rep_one_iso ), |
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(abs_one_iso RS allI) RS ((rep_one_iso RS allI) |
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RS iso_strict) RS conjunct1] )1) |
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]); |
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val one_when = map prover ["one_when`x`UU = UU","one_when`x`one = x"]; |
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